Question

Решить систему линейных уравнений методом гаусса, буду . 5х-6у+29z=32 4x-3y+24z=30 2x+y+7z=15

Answer 1

$\left(\begin{array}{ccc|c}5&-6&29&32\\4&-3&24&30\\7&1&7&15\end{array}\right)\Rightarrow \left(\begin{array}{ccc|c}1&-1,2&5,8&6,4\\4&-3&24&30\\7&1&7&15\end{array}\right)\Rightarrow\\\Rightarrow \left(\begin{array}{ccc|c}1&-1,2&5,8&6,4\\0&1,8&0,8&4,4\\0&3,4&-4,6&2,2\end{array}\right)\Rightarrow\left(\begin{array}{ccc|c}1&-1,2&5,8&6,4\\0&1&\frac49&\frac{22}9\\0&3,4&-4,6&2,2\end{array}\right)\Rightarrow$
$\Rightarrow\left(\begin{array}{ccc|c}1&0&\frac{19}3&\frac{28}3\\0&1&\frac49&\frac{22}9\\0&0&-\frac{55}9&-\frac{55}9\end{array}\right)\Rightarrow\left(\begin{array}{ccc|c}1&0&\frac{19}3&\frac{28}3\\0&1&\frac49&\frac{22}9\\0&0&1&19\end{array}\right)\Rightarrow\\\Rightarrow\left(\begin{array}{ccc|c}1&0&0&3\\0&1&0&2\\0&0&1&1\end{array}\right)\\x=3,\;y=2,\;z=1$